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3 Answers
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In Spanish it is mandatory to use a before the Direct Object in most cases when it refers to a person or persons. You can find a full explanation in the Diccionario Panhispánico de Dudas.

Your example would be covered by case 1.1.e in the link above if you were talking about people; but, of course, a cat and a horse are not such a thing. So the correct translation is:

Oí un gato y un caballo.

If you write Oí a un gato y a un caballo, you are somehow assimilating them to people. At least, you are implying an affective affinity with them. Since this is not the case (you are talking about an unknown cat and horse), I would advise not to use a in this sentence. Compare this with the case when you heard, for instance, your aunt's cat. This is an animal you know and you can express this affective affinity using a:

This is much more common in Spanish, in particular it would be odd style in English to say Heard to a horse (it would be either Heard a horse or Listened to a horse). Instead Spanish is a bit more liberal, consider: ¿Cómo entrenar a un perro? and ¿Cómo entrenar un perro? both are acceptable.

Note 1: using xe as a gender agnostic pronoun to denote the fact that the gender of the person - the one who sees in the given phrase - cannot be infered.

Note 2: In English you will probably not specify the flute is a transverse flute (side-blown flute). Yet in Spanish - at least in some regions - the world flauta often refer to a fipple flute, more properly to a "recorder" (this is known as flauta dulce - literally sweet flute) because these are very common.

As counterexample consider:

- Escuché un ruido -- I heard a noise
x Escuché a un ruido -- I heard/listened to a noise

Note: Although Escucchar is usually Listen it is common to use it for a sound that caught your attention.